rohit placed a pencil perpendicular to principal axis in front of converging mirror of focal length 30 cm the image is twice the size of the pencil . calculate the distance of the object from the mirror
Answers
Explanation:
Rohit placed a pencil perpendicular to a principle axis in front of a converging mirror (Another name Concave mirror) of focal length 30 cm. The image formed (h') is twice the size of the pencil (h). Calculate distance of the object from the mirror (u).
Means...
f = - 30 cm
[We have given that mirror is converging means concave mirror. And Image formed is twice the size of the object. Means image formed is behind the mirror and is larger in size. So, we take f in -ve sign.]
h' = 2h
u = ?
Now;
m = \dfrac{-v}{u}
u
−v
= \dfrac{h'}{h}
h
h
′
\dfrac{-v}{u}
u
−v
= \dfrac{2h}{h}
h
2h
\dfrac{-v}{u}
u
−v
= 2
-v = 2u
v = - 2u
As we know that...
\dfrac{1}{f}
f
1
= \dfrac{1}{v}
v
1
+ \dfrac{1}{u}
u
1
\dfrac{1}{-30}
−30
1
= \dfrac{1}{-2u}
−2u
1
+ \dfrac{1}{u}
u
1
\dfrac{-1}{30}
30
−1
= \dfrac{-1}{2u}
2u
−1
+ \dfrac{-\:1\:+\:2}{2u}
2u
−1+2
\dfrac{-1}{30}
30
−1
= \dfrac{+1}{2u}
2u
+1
2u = - 30 cm
u = - 15 cm
Answer
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» Given
Rohit placed a pencil perpendicular to a principle axis in front of a converging mirror (Another name Concave mirror) of focal length 30 cm. The image formed (h') is twice the size of the pencil (h). Calculate distance of the object from the mirror (u).
Means...
f = - 30 cm
[We have given that mirror is converging means concave mirror. And Image formed is twice the size of the object. Means image formed is behind the mirror and is larger in size. So, we take f in -ve sign.]
h' = 2h
u = ?
Now;
m = =
=
= 2
-v = 2u
v = - 2u
As we know that...
= +
= +
= +
=
2u = - 30 cm
u = - 15 cm